1. Consider a two-period probabilistic inventory model in which the demand is backlogged, and orders are received with zero delivery lag. The demand pdf per period is uniform between 0 and 10, and the cost parameters are given as Unit selling price = $2 Unit purchase price = $1 Unit holding cost per month = $.10 Unit penalty cost per month = $3 Discount factor = .8 Find the optimal inventory policy for the two periods, assuming that the initial inventory for period 1 is zero.